Of course, ideas, fads, technologies, and behavior patterns do not just come and spread, they often decline.  Perhaps the most obvious is replacement.  Some idea or technology catches on and propagate only to be later replaced with something perceived to be better.  I use the word “perceived,” not because I think the new and improved is not better.  I generally believe that the perception is correct.  But, I want to emphasize that meme population dynamics is based upon perception and not reality.  When the perception is incorrect, reality may intervene and demonstrate the perception to be incorrect and the perception may change.

Consider equation 10.3 that describes competition between two memes.

Let us see if these equations can describe the replacement of one technology, fashion, or fad with another.

Let  be the number of copies of a meme for a particular technology or fashion fad and let  be the number of memes of a potential replacement meme.  They might represent the transition from water wheel to steam engine as the source of power for factories.  Or, they might represent the changing lengths of women’s skirts, or the replacement of the skirt with slacks.  We can think of  and  as determined by the perceived value of each meme.  

At time  let  and .   will increase according to the logistics curve with an upper bound of N.  N is the number of entities that can acquire meme 1.  Let us assume that there is a time () where this has occurred, with the exception of one creative individual who develops meme 2.  At this point equations 10.3 become

In competition a meme cannot replace another meme.  If our creative individual develops meme 2 before meme1 has spread to everyone else then meme 2 will be adopted by some of the population that has not acquired meme 1.  But at no time can any of the equations 10.1 through 10.5 describe meme replacement. 

To accommodate meme replacement we must add what corresponds in population dynamics to death.  If we are to be accurate we must tread slowly here.  When I was in school I acquired the slide rule use memes.  Even though, I now use a calculator, I have not lost the slide rule meme set.  Today aspiring scientists and engineers do not acquire the slide rule memes; they go directly to acquiring the calculator memes.  I as an individual do not lose memes because I adopt a new meme.  Because memory is fallible and skill requires practice, I may lose memes, but not because I acquire another.  At the society level the percentage of individuals with a copy of a meme does decline as a result of meme replacement, since the replaced meme is never acquired by new members of the population.  For the moment let us ignore this intermediate of step and say that a meme that is no longer used by an individual has effectively disappeared.  We can then write the competitive replacement equation as

                                                              (10.6)

where  is the rate of replacement of meme 1 by meme 2 and  is the rate of replacement of meme 2 with meme 1.  If , then  and , which to say that meme 2 has replaced meme 1.

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(C) 2005-2014 Wayne M. Angel.  All rights reserved.